In retaliation, one of Capcom's artist drew an artwork of Sagat holding a defeated opponent by the head during the release of Street Fighter II': Champion Edition. The defeated opponent wore an attire similar Ryo's: an orange karate gi with a torn black shirt underneath and geta sandals; but had long dark hair tied to a ponytail like Robert Garcia, another character from the Art of Fighting series. This character design would become the basis of Dan, who was introduced as a secret character in Street Fighter Alpha. His fireball is telling: instead of using both hands to unleash his Gadouken (as Ryu and Ken do for the Hadouken), he propels it with one hand, like Ryo, Robert and Yuri do for the Kooh-ken. Dan can also taunt infinitely like the Art of Fighting games, unlike his fellow Street Fighter Alpha characters.
After the events of Street Fighter Alpha and Street Fighter Alpha 2, Dan believed he had achieved his revenge by defeating Sagat (who had actually thrown the fight), and his motivation switched to promoting and expanding his Saikyo-style school, even to the point of offering exercise videos and correspondence courses. He has seemingly had some limited success promoting Saikyo-style.
In SFA3, he was Sakura Kasugano's supposed sensei, who followed him around in order to meet Ryu. He's also good friends with Blanka too, since Blanka saved Dan during the events of Sakura Ganbaru! manga.
Despite being the weakest of all the main characters, Dan is still an above-average martial artist when compared to typical fighters. In the first volume of the manga Sakura Ganbaru!, Dan enters a street fighting competition and is shown doing rather well, only losing to Ken, who later went on to win the entire competition.
In Dan's ending in Marvel Super Heroes vs. Street Fighter, Dan's sister appears to prevent him finishing off Cyber-Akuma saying "Don't you know who he is? He's our...", parodying the ending of the original Art of Fighting where Ryo was about to kill Mr. Karate before being told he is their father by Yuri (Dan's sister even looks like her). 
One of Dan's win quotes in Street Fighter Alpha 3 is "I hate the art of fighting, but I want to be the king of fighters!" This was a direct reference to Art of Fighting and The King of Fighters series by SNK.
Also Dan's fighting style, the Saikyo-ryuu, is a parody of Kyokugen-ryuu, the fighting style used by Ryo and Robert. To further the parody, Saikyo-ryuu means "Strongest style" while Kyokugen-ryuu means "Extreme Style."
In the SNK vs. Capcom series (more specifically in SVC Chaos: SNK vs. Capcom), there is a running gag where Dan is often mistaken for Ryo or Robert, even by himself in a mirror match (Kasumi Todoh is one example: even after Dan tells her he is not Robert, she still does not believe him). In these games, Dan parodies even more of Ryo's attacks. He also mistook Mr. Karate for his father's ghost (though, in his ending in Neo Geo Pocket's SNK vs. Capcom: The Match of the Millennium, he seems to acknowledge that Takuma and Go are different people). In Ryo's ending for Capcom vs. SNK 2, it is hinted that Dan came to the Sakazakis' Kyokugenryu Karate school to sign up. In Pocket Fighter, Dan can call on the ghost of his father, whose face resembles the same tengu mask as Mr. Karate. This is mirrored in Capcom's official artwork for Street Fighter Alpha; earlier works featured Dan's father as wearing a tengu mask while later ones show that the long nose was indeed a feature of Go Hibiki. All other instances of Go Hibiki's face are obscured, such as the image of young Sagat clutching Go's face.
Though his fighting stance is similar to Ken and Ryu's, it is more "loose" and animated. Many of his mannerisms directly mirror those of Yuri Sakazaki.
Dan has a move known as the Hisshou Buraiken (Complete and Total Victory Relying on Nobody but Myself Fist), a standing parody of Ryo's flying Desperation move, the Ryuuko Ranbu. Dan also possesses a "Shoryu Reppa" type move called the Koryu Rekka (Shiny Dragon Blaze), which was borrowed from the double uppercut at the end of Ryo's MAX Ryuuko Ranbu (he even imitates Ryo's "Kyokugen-ryuu Ougi!"/"Kyokugen-style secret!" yell that is used at the beginning of Ryuuko Ranbu, instead declaring "Saikyo-ryuu Ougi!"). Both moves have little to no range at all, and leave Dan wide open for attack if the moves are blocked.
Dan is one of only two characters in the Street Fighter series that has a super taunt, along with Sagat: Chouhatsu Densetsu (Legendary Taunt) and Chouhatsu Shinwa (Mythical Taunt).
Dan has a move known as the Otoko Michi (Path of a Man) which parodies Akuma's Shun Goku Satsu. The Otoko Michi is performed by doing the command for the Shun Goku Satsu in reverse. Depending on the game, the Otoko Michi can be as powerful as the Shun Goku Satsu, which can take off more than half of the opponent's lifebar, or it takes off a minimal amount of life from the opponent. In most versions, it leaves Dan with only 1% of his own life. Due to its slow speed and high costs, this move is considered highly unreliable and only used when absolute victory is certain. In Marvel vs. Capcom 2, it is the strongest single Hyper Combo in the game. In SVC Chaos: SNK vs. Capcom, it not only does a considerable amount of damage when used, but he loses no life from performing it: this is due to the fact that it is his Exceed attack, all of which can only be done once per match and need a low amount of life remaining to become usable to begin with.
Coincidentally, Dan parodies even more Kyokugen-style attacks in the SNK-produced games of the SNK vs. Capcom series. He gains the Gadou Sho Ko Ken (a Gadoken-ranged version of the Haoh Sho Koh Ken) in both SNK-produced games (as a Level 2 version of Shinkuu Gadoken in The Match of the Millennium, and a regular special move in SVC Chaos). In SVC Chaos: SNK vs. Capcom, he also gains a parody version of Ryo's Tenchi Haou Ken called Kyuukyoku Tenchi Gadou Zuki that is able to block any attack during the charge-up period, even normally unblockable moves, but does not do much damage and has an extremely long recovery time since Dan punches the opponent so hard that he breaks the bones in his hand, and needs a moment to tend to it.
A running gag in all games that Dan appears in is his ability to taunt. In games where the player is limited to only one taunt, Dan is able to do an unlimited amount. Each Taunt also adds to his Super bar, generally (it varies by game) by a healthy amount. He is also able to perform the infamous "Super Taunt" (Chohatsu Dentetsu), which is simply a taunt dragged out for several seconds. It does absolutely no damage, and Dan is vulnerable throughout the entire escapade. It takes a whole Super bar/level to perform. This attack is often seen as the ultimate insult, as it shows the player's confidence in victory enough to make him waste a chance at using a super move in favor of preforming something with no practical value whatsoever.
In Marvel Super Heroes vs. Street Fighter, one can input a code just before the start of the match, in which Dan falls onto the ground, creating a comically huge explosion, instead of his normal entrance. He then gets up and the fight starts. This has absolutely no effect on gameplay.